Image analysis method and image analysis apparatus

ABSTRACT

An image analysis method includes acquiring an image of at least one frame that comprises pixels, setting at least one analytic region for the image of at least one frame, extracting data on the pixel corresponding to each analytic region, setting time intervals for data pairs for use in correlation calculations, performing a correlation calculation for each of the time intervals by use of the extracted data, and performing a fitting for each of the correlation calculation results.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation application of PCT Application No.PCT/JP2012/075841, filed Oct. 4, 2012 and based upon and claiming thebenefit of priority from prior Japanese Patent Applications No.2011-246462, filed Nov. 10, 2011, the entire contents of which areincorporated herein by reference.

BACKGROUND

1. Field of the Invention

The present invention relates to an image analysis method and an imageanalysis apparatus.

2. Description of the Related Art

A technique for an image analysis called fluorescence cross-correlationspectroscopy (FCCS) has heretofore been known. The FCCS is shown in, forexample, Jpn. Pat. Appln. KOKAI Publication No. 2007-093277. Accordingto the FCCS, excitation light is continuously applied to one or moremeasurement points in a sample for a given length of time (e.g. for 10seconds), and fluctuations of the intensity of fluorescence emitted fromthe measurement points are detected and correlatively analyzed toestimate the number of molecules and a diffusion constant.

A technique for an image analysis called a raster image correlationspectroscopy (RICS) has been also known. The RICS is shown in, forexample, “Measuring Fast Dynamics in Solutions and Cells with a LaserScanning Microscope”, Michelle A. Digman, Claire M. Brown, ParijatSengupta, Paul W. Wiseman, Alan R. Horwitz, and Enrico Gratton,Biophysical Journal, Vol. 89, P 1317-1327, August 2005. According to theRICS, one or more frames of raster scan images are acquired. The rasterscan images may be, for example, fluorescence images. Data regardingeach pixel of the fluorescence images represents information on theintensity of fluorescence generated from a point in a correspondingsample. The data regarding the pixels vary in the time and position ofacquisition.

Correlation characteristics dependent on the fluctuations of moleculesare obtained by a spatial autocorrelation analysis using the dataregarding the pixels. A diffusion constant and the number of moleculescan be found from the correlation characteristics of the molecules. Amolecular diffusion time can be found from the diffusion constant.

Since the diffusion time and the number of molecules can be thusevaluated by the spatial autocorrelation analysis, an interactionbetween the molecules can be observed.

SUMMARY

An image analysis method according to the present invention comprisesacquiring an image of at least one frame that comprises pixels, settingat least one analytic region for the image of at least one frame,extracting data on the pixel corresponding to each analytic region,setting time intervals for data pairs for use in correlationcalculations, performing a correlation calculation for each of the timeintervals by use of the extracted data, and performing a fitting foreach of the correlation calculation results.

Advantages of the invention will be set forth in the description whichfollows, and in part will be obvious from the description, or may belearned by practice of the invention. The advantages of the inventionmay be realized and obtained by means of the instrumentalities andcombinations particularly pointed out hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constituteapart of the specification, illustrate embodiments of the invention, andtogether with the general description given above and the detaileddescription of the embodiments given below, serve to explain theprinciples of the invention.

FIG. 1 schematically shows an image analysis apparatus according to oneembodiment;

FIG. 2 shows functional blocks of a control section shown in FIG. 1;

FIG. 3 is a flowchart of an image analysis according to one embodiment;

FIG. 4 shows a fluorescence image of a two-dimensional image of oneframe;

FIG. 5 shows fluorescence images of a three-dimensional image of oneframe;

FIG. 6 shows images of observation regions of frames and an extractedimage of one analytic region;

FIG. 7 shows images of observation regions of frames and extractedimages of two analytic regions;

FIG. 8 schematically shows a correlation calculation for the sameanalytic region in the image of the same frame;

FIG. 9 schematically shows a correlation calculation for the sameanalytic region in the images of different frames;

FIG. 10 schematically shows a correlation calculation for differentanalytic regions in the image of the same frame;

FIG. 11 schematically shows a correlation calculation for differentanalytic regions in the images of different frames;

FIG. 12 is an image in which a calculation result of a spatialcross-correlation value regarding molecules in a sample is indicated byluminance; and

FIG. 13 shows a fitting result of the calculation result of the spatialcross-correlation value in FIG. 12.

DESCRIPTION OF EMBODIMENT

An embodiment of the present invention will now be described withreference to the drawings.

[Apparatus Configuration]

FIG. 1 schematically shows an image analysis apparatus according to oneembodiment. This image analysis apparatus has a configuration based on ascanning confocal optical microscope for a fluorescence observation of asample.

As shown in FIG. 1, an image analysis apparatus 100 has a lightapplication section 110 to apply light such as excitation light to asample S, a light detection section 130 to detect light such asfluorescence from the sample S, a control section 160 to perform controlnecessary for an image analysis, and a sample stage 190, which supportsthe sample S.

The sample S is contained in a sample container such as a microplate ora slide glass, and mounted on the sample stage 190. The sample stage 190supports, for example, the sample S movably in a lateral direction(xy-direction) and in a height direction (z-direction) relative to thelight application section 110 and the light detection section 130. Forexample, the sample stage 190 includes three stepping motors havingtheir output shafts that intersect at right angles with one another. Thesample S can be moved in the xyz-direction by these stepping motors.

The image analysis apparatus 100 is, for example, a multiple lightirradiation-multiple light detection type. Thus, the light applicationsection 110 includes an n-channel light source section 111, and thelight detection section 130 includes an m-channel light detectionsection 131. The light source section 111 has n channels, and canradiate excitation light beams of n kinds of different wavelengths. Thelight detection section 131 has m channels, and can detect fluorescenceof m kinds of different wavelengths. The light source section 111 doesnot always need to have more than one channel, and may only have onechannel. The light detection section 131 does not always need to havemore than one channel, and may only have one channel.

The n-channel light source section 111 of the light application section110 includes light sources 112 a, . . . , 112 n, collimating lenses 114a, . . . , 114 n, and dichroic mirrors 116 a, . . . , 116 n. The lightsources 112 a, . . . , 112 n emit excitation light to excite fluorescentdyes included in the sample S to the sample S to emit light(fluorescence). The wavelengths of the excitation light emitted from thelight sources 112 a, . . . , 112 n are different from one another tocorrespond to the kinds of fluorescent dyes included in the sample S.The light sources 112 a, . . . , 112 n comprise, for example, laserlight sources of oscillation wavelengths corresponding to thefluorescent dyes in the sample S. The collimating lenses 114 a, . . . ,114 n collimate the excitation light emitted from the light sources 112a, . . . , 112 n, respectively. The dichroic mirrors 116 a, . . . , 116n reflect, in the same direction, the excitation light that has passedthrough the collimating lenses 114 a, . . . , 114 n, respectively. Thedichroic mirrors 116 a, . . . , 116 n respectively transmit theexcitation light entering from the upper side in FIG. 1, and reflect theexcitation light entering from the right side in FIG. 1. As a result,the excitation light of different wavelengths respectively emitted fromthe light sources 112 a, . . . , 112 n are combined into a beam afterpassing through the dichroic mirror 116 a. The dichroic mirror 116 ndoes not need to transmit the excitation light, and may therefore bechanged to a simple mirror.

The light application section 110 further includes a dichroic mirror122, a galvano-mirror 124, an objective lens 126, and an objective lensdrive mechanism 128. The dichroic mirror 122 reflects the excitationlight from the light source section 111 to the galvano-mirror 124, andtransmits the fluorescence emitted from the sample S. The galvano-mirror124 reflects the excitation light to the objective lens 126, and changesits reflection direction. The objective lens 126 converges theexcitation light and then applies the excitation light to a measurementpoint in the sample S, and takes in the light from the measurement pointin the sample S. The objective lens used as the objective lens 126 has ahigh numerical aperture (NA) to form a micro confocal region(measurement point). The confocal region to be thereby obtained has asubstantially cylindrical shape that is sized at approximately 0.6 μm indiameter (in an xy-plane) and approximately 2 μm length (in thez-direction). The galvano-mirror 124 constitutes an xy-scan mechanism toscan the measurement point in the xy-direction. The xy-scan mechanismmay be constituted by using a acoustooptical modulator (AOM), a polygonmirror, or a hologram scanner instead of the galvano-mirror. Theobjective lens drive mechanism 128 moves the objective lens 126 alongthe optical axis. As a result, the measurement point is moved in thez-direction. That is, the objective lens drive mechanism 128 constitutesa z-scan mechanism to scan the measurement point in the z-direction.

The light detection section 130 and the light application section 110commonly include the objective lens 126, the galvano-mirror 124, and thedichroic mirror 122. The light detection section 130 further includes aconverging lens 132, a pin hole 134, and a collimating lens 136. Theconverging lens 132 converges the light that has passed through thedichroic mirror 122. The pin hole 134 is located in the focus of theconverging lens 132. That is, the pin hole 134 is located at a positionthat is conjugate to the measurement point in the sample S, andselectively allows only the light from the measurement point to passtherethrough. The collimating lens 136 collimates the light that haspassed through the pin hole 134. The light that has passed through thecollimating lens 136 enters the m-channel light detection section 131.

The m-channel light detection section 131 includes dichroic mirrors 138a, . . . , 138 m, fluorescence filters 140 a, . . . , 140 m,photodetectors 142 a, . . . , 142 m. The dichroic mirrors 138 a, . . . ,138 m selectively reflect light of wavelengths located in the vicinityof the wave range of the fluorescence to be detected, respectively. Thedichroic mirror 138 m does not need to transmit the light, and maytherefore be changed to a simple mirror. The fluorescence filters 140 a,. . . , 140 m respectively cut off the light of undesired wavelengthcomponents out of the light reflected by the dichroic mirrors 138 a, . .. , 138 m, and selectively transmit the fluorescence generated by theexcitation light from the light sources 112 a, . . . , 112 n. Thefluorescence that has passed through the fluorescence filters 140 a, . .. , 140 m enter the photodetectors 142 a, . . . , 142 m, respectively.The photodetectors 142 a, . . . , 142 m output signals corresponding tothe intensities of the light that has entered. That is, thephotodetectors 142 a, . . . , 142 m output fluorescence intensitysignals from the measurement point in the sample S.

The control section 160 comprises, for example, a personal computer. Thecontrol section 160 performs the acquisition, storage, and display offluorescence images of observation regions of the sample S, waiting foran input such as a setting of an analytic region, and analyticprocessing of images (e.g. calculation of a correlation value, andestimation of the number of molecules and a diffusion time). The controlsection 160 also controls the galvano-mirror 124, which is the xy-scanmechanism, the objective lens drive mechanism 128, which is the z-scanmechanism, and the sample stage 190.

Functional blocks of the control section shown in FIG. 1 are shown inFIG. 2. As shown in FIG. 2, the control section 160 includes a scancontrol section 162, an image formation section 164, a storage section166, a display section 168, an input section 170, an analytic regionsetting section 172, a data extraction section 174, an analyticprocessing section 178, a time interval setting section 178, and a stagecontrol section 180. The scan control section 162, the image formationsection 164, the storage section 166, and the stage control section 180cooperate with the light application section 110 and the light detectionsection 130 described above to constitute an image acquisition section.

The scan control section 162 controls the galvano-mirror 124 toraster-scan an application position of the excitation light in thesample S when a fluorescence image of the sample S is acquired. Ifnecessary, the scan control section 162 also controls the objective lensdrive mechanism 128 to z-scan the application position of the excitationlight in the sample S. The image formation section 164 forms afluorescence image of the sample S from information on the applicationposition of the excitation light input from the scan control section 162and output signals of the photodetectors 142 a, . . . , 142 m. As aresult, the fluorescence image is acquired. The fluorescence imageformed by the image formation section 164 is stored in the storagesection 166. The display section 168 displays the fluorescence image ofthe sample S and an analytic processing result. The input section 170includes, for example, a mouse and a keyboard, and cooperates with thedisplay section 168 to constitute a GUI. This GUI is used to set anobservation region and an analytic region. The stage control section 180controls the sample stage 190 in accordance with input information fromthe input section 170 to set, for example, an observation region. Theanalytic region setting section 172 sets an analytic region inaccordance with input information from the input section 170. The dataextraction section 174 extracts data on the analytic region for whichcorrelation calculations are to be performed. The time interval settingsection 176 sets time intervals of pairs of data used in the correlationcalculations. The analytic processing section 178 performs thecorrelation calculations by using data on the pixels of the image of theanalytic region. The processing in the analytic processing section 178will be described in detail later.

As shown in FIG. 1, the excitation light emitted from the light sources112 a, . . . , 112 n is applied to the measurement point in the sample Sthrough the collimating lenses 114 a, 114 n, the dichroic mirrors 116 a,. . . , 116 n, the dichroic mirror 122, the galvano-mirror 124, and theobjective lens 126. The measurement point to which the excitation lightis applied is raster-scanned with the galvano-mirror 124 in thexy-direction. If necessary, the measurement point is z-scanned with theobjective lens drive mechanism 128 whenever one raster-scan ends. Themeasurement point is scanned over the whole observation region. Thesample S that has received the excitation light generates fluorescencefrom the measurement point. The light (including undesired reflectedlight in addition to the fluorescence) from the sample S reaches the pinhole 134 through the objective lens 126, the galvano-mirror 124, thedichroic mirror 122, and the converging lens 132. Since the pin hole 134is located at the position that is conjugate to the measurement point,the light from the measurement point in the sample S only passes throughthe pin hole 134. The light that has passed through the pin hole 134,that is, the light from the measurement point in the sample S enters them-channel light detection section 131 through the collimating lens 136.The light that has entered the m-channel light detection section 131 issplit (i.e. dispersed) in accordance with the wavelengths by thedichroic mirrors 138 a, . . . , 138 m, and undesired components areremoved by the fluorescence filters 140 a, . . . , 140 m. Thefluorescence that has passed through the fluorescence filters 140 a, . .. , 140 m enters the photodetectors 142 a, . . . , 142 m, respectively.The photodetectors 142 a, . . . , 142 m respectively output fluorescenceintensity signals indicating the intensities of the incident light, thatis, the fluorescence emitted from the measurement point in the sample S.The fluorescence intensity signals are input to the image formationsection 164. The image formation section 164 processes the inputfluorescence intensity signals synchronously with positional informationin the xy-direction (and the z-direction) to form a fluorescence imageof the observation region in the sample S. The formed fluorescence imageis saved in the storage section 166. The fluorescence image saved in thestorage section 166 is displayed on the display section 168 as it is, orprocessed by the analytic processing section 178, and an analyticprocessing result is displayed on the display section 168.

[Analytic Procedure]

A procedure of an image analysis is described below with reference toFIG. 3. Steps are described by proper reference to FIG. 4 to FIG. 11.

(Step S1)

An image or images, for example a fluorescence image or fluorescenceimages, of a frame or frames of the observation region of the sample Sis acquired. The fluorescence image is acquired through one channel ofthe light source section 111, and one channel of the light detectionsection 131 corresponding thereto. The fluorescence image of each framecomprises pixels the data of which have been acquired in a time-seriesmanner by the scan of the excitation light. The measurement pointactually has spatial expansions in the xyz-direction, and the pixel hasa size corresponding to the spatial expansions of the measurement point.The data on each pixel of the fluorescence image is, for example, theintensity of the fluorescence emitted from the corresponding measurementpoint.

The observation region is a two-dimensional region or athree-dimensional region, and the fluorescence image is atwo-dimensional image or a three-dimensional image accordingly. When theobservation region is the two-dimensional region, the fluorescence imageis the two-dimensional image in which pixels having sizes in thexy-direction are two-dimensionally arranged. When the observation regionis the three-dimensional region, the fluorescence image is thethree-dimensional image in which pixels having sizes in thexyz-direction are three-dimensionally arranged. From a different pointof view, the three-dimensional image comprises two-dimensional images offrames having different z-positions.

A fluorescence image of a two-dimensional image of one frame is shown inFIG. 4. In FIG. 4, τ_(p) is the difference (pixel time) of acquisitiontime between a certain pixel and a next pixel adjacent thereto. That is,the pixel time τ_(p) is a time required to acquire data for one pixel.τ_(l) is the difference (line time) of acquisition time between aninitial pixel of a certain line and an initial pixel of a next line.That is, the line time τ_(l) means a time required to scan one line.

A three-dimensional image of one frame is shown in FIG. 5. In FIG. 5,τ_(p) is a pixel time, τ_(l) is a line time, and τ_(f) is the difference(frame time) of acquisition time between an initial pixel of a certainframe and an initial pixel of a next frame. That is, the frame timeτ_(f) means a time required to scan one frame.

(Step S2)

One or more analytic regions are set for the image, for example, thefluorescence image of the observation region of one frame or each offrames that has been acquired. The analytic regions are spatiallydifferent regions, and are normally separate from one another and do notoverlap. The analytic region is a two-dimensional region for atwo-dimensional observation region, and is normally a three-dimensionalregion but may be a two-dimensional region for a three-dimensionalobservation region. In FIG. 6, when 100 frames are acquired, oneanalytic region A₁ is set for a fluorescence image of the observationregion of each of frames f₁ to f₁₀₀), and the analytic region A₁ islocated outside a nucleus of a cell. In FIG. 7, two analytic regions A₁and A₂ are set for a fluorescence image of the observation region ofeach of frames f₁ to f₁₀₀), and the analytic region A₁ is locatedoutside a nucleus of a cell, while the analytic region A₂ is locatedinside the nucleus of the cell.

(Step S3)

Data on the pixel corresponding to each analytic region is extracted. InFIG. 6, the extracted data, that is, images of the pixels of theanalytic region A₁ of the frames f₁ to f₁₀₀ are shown. In FIG. 7, theextracted data, that is, images of the pixels of the analytic regions A₁and A₂ of the frames f₁ to f₁₀₀) are shown.

(Step S4)

Time intervals (delay times) of data pairs for use in correlationcalculations are set. Each time interval corresponds to the different ofacquisition time of the data on pixels of the pairs used in aproduct-sum calculation for each correlation calculation. For example,one time interval corresponds to two pixels in the same analytic regionor different analytic regions of the same frame, and another timeinterval corresponds to two pixels in the same analytic region ordifferent analytic regions of different frames. These time intervals arepreferably set so that a sufficient number of product-sum calculationscan be performed.

(Step S5)

The extracted data on the pixels are used to perform the correlationcalculations. The calculation formula used in the correlationcalculations varies by whether the image of the analytic region is thetwo-dimensional image or the three-dimensional image. Moreover, thecalculation formula varies by whether two pixels of each of data pairsfor use in the product-sum calculations of the correlation calculationbelong to the same analytic region or different analytic regions. Inaddition, the calculation formula varies by whether two pixels of eachof data pairs for use in the product-sum calculations of the correlationcalculation belong to the image of the same frame or the images ofdifferent frames.

The calculation formulas to be applied to the two-dimensional image areas follows.

1. Two pixels of each data pair belong to the image of the same analyticregion, and belong to the image of the same frame. In this case, pairsof data on the pixels in the same analytic region in the image of thesame frame are used to perform a correlation calculation. Thiscorrelation calculation is an autocorrelation calculation. FIG. 8schematically shows the correlation calculation in this case.

$\begin{matrix}{{G_{2\;{ssa}}\left( {\xi,\psi} \right)} = \frac{\sum\;{{I_{f_{i}}\left( {x,y} \right)}*{{I_{f_{i}}\left( {{x + \xi},{y + \psi}} \right)}/M_{ii}}}}{\left( {\sum{{I_{f_{i}}\left( {x,y} \right)}/M_{i}}} \right)^{2}}} & (1)\end{matrix}$where G_(2ssa) is an autocorrelation value in the same analytic regionA₁ of the same frame f_(i), I_(fi) is data, for example, fluorescenceintensity data on the pixels of the image of the analytic region A₁ ofthe frame f_(i), x, y are spatial coordinates of a measurement point, ξ,ψ are variations of the spatial coordinates from the measurement point,M_(ii) is the number of product-sum calculations of the data on thepixels of the image of the analytic region A₁ of the frame f_(i), andM_(i) is the total number of data on the pixels of the image of theanalytic region A₁ of the frame f_(i).

2. Two pixels of each data pair belong to the image of the same analyticregion, and belong to the images of different frames. In this case,pairs of data on the pixels in the same analytic region in the image ofthe same frame are used to perform a correlation calculation. Thiscorrelation calculation is a cross-correlation calculation. FIG. 9schematically shows the correlation calculation in this case.

$\begin{matrix}{{G_{2\;{sdc}}\left( {\xi,\psi} \right)} = \frac{\sum\;{{I_{f_{i}}\left( {x,y} \right)}*{{I_{f_{j}}\left( {{x + \xi},{y + \psi}} \right)}/M_{ij}}}}{\left( {\sum{{I_{f_{i}}\left( {x,y} \right)}/M_{i}}} \right)\left( {\sum{{I_{f_{j}}\left( {x,y} \right)}/M_{j}}} \right)}} & (2)\end{matrix}$where G_(2sdc) is a cross-correlation value in the same analytic regionA₁ of a frame f_(i) and a frame f_(j) that are different from eachother, I_(fi) is data, for example, fluorescence intensity data on thepixels of the image of the analytic region A₁ of the frame f_(i), I_(fj)is data, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₁ of the frame f_(i), x, y are spatialcoordinates of a measurement point, ξ, ψ are variations of the spatialcoordinates from the measurement point, M_(ij) is the number ofproduct-sum calculations of the data on the pixels of the image of thesame analytic region A₁ of the frame f_(i) and frame f_(j), M_(i) is thetotal number of data on the pixels of the image of the analytic regionA₁ of the frame f_(i), and M_(j) is the total number of data on thepixels of the image of the analytic region A₁ of the frame f_(j).

3. Two pixels of each data pair belong to the images of differentanalytic regions, and belong to the image of the same frame. In thiscase, pairs of data on the pixels in different analytic regions in theimages of different frames are used to perform a correlationcalculation. This correlation calculation is a cross-correlationcalculation. FIG. 10 schematically shows the correlation calculation inthis case.

$\begin{matrix}{{G_{2\;{dsc}}\left( {\xi,\psi} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y} \right)}*{{I_{2f_{i}}\left( {{x + \xi},{y + \psi}} \right)}/M_{12\;{ii}}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{i}}\left( {x,y} \right)}/M_{2i}}} \right)}} & (3)\end{matrix}$where G_(2dsc) is a cross-correlation value between different analyticregions A₁ and A₂ of the same frame f_(i), I_(1fi) is data, for example,fluorescence intensity data on the pixels of the image of the analyticregion A₁ of the frame f_(i), I_(2fi) is data, for example, fluorescenceintensity data on the pixels of the image of the analytic region A₂ ofthe frame f_(i), x, y are spatial coordinates of a measurement point, ξ,ψ are variations of the spatial coordinates from the measurement point,M_(12ii) is the number of product-sum calculations of the data on thepixels of the images of the different analytic regions A₁ and A₂ of theframe f_(i), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2i) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(i).

4. Two pixels of each data pair belong to the images of differentanalytic regions, and belong to the image of the different frame. Inthis case, pairs of data on the pixels in different analytic regions inthe images of different frames are used to perform a correlationcalculation. This correlation calculation is a cross-correlationcalculation. FIG. 11 schematically shows the correlation calculation inthis case.

$\begin{matrix}{{G_{2{ddc}}\left( {\xi,\psi} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y} \right)}*{{I_{2f_{j}}\left( {{x + \xi},{y + \psi}} \right)}/M_{12{ij}}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{j}}\left( {x,y} \right)}/M_{2j}}} \right)}} & (4)\end{matrix}$where G_(2ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fi) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y are spatialcoordinates of a measurement point, ξ, ψ are variations of the spatialcoordinates from the measurement point, M_(12ij) is the number ofproduct-sum calculations of the data on the pixels of the images of theanalytic region A₁ of the frame f_(i) and the analytic region A₂ of theframe f_(j), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2j) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(j).

The calculation formulas to be applied to the three-dimensional imageare as follows.

1. Two pixels of each data pair belong to the image of the same analyticregion, and belong to the image of the same frame. In this case, pairsof data on the pixels in the same analytic region in the image of thesame frame are used to perform a correlation calculation. Thiscorrelation calculation is an autocorrelation calculation.

$\begin{matrix}{{G_{3{ssa}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{f_{i}}\left( {x,y,z} \right)}*{{I_{f_{i}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{ii}}}}{\left( {\sum{{I_{f_{i}}\left( {x,y,z} \right)}/M_{i}}} \right)^{2}}} & (5)\end{matrix}$where G_(3ssa) is an autocorrelation value of the same analytic regionA₁ of the same frame f_(i), I_(fi) is data, for example, fluorescenceintensity data on the pixels of the image of the analytic region A₁ ofthe frame f_(i), x, y, z are spatial coordinates of a measurement point,ξ, ψ, η are variations of the spatial coordinates from the measurementpoint, M_(ii) is the number of product-sum calculations of the data onthe pixels of the image of the analytic region A₁ of the frame f_(i),and M_(i) is the total number of data on the pixels of the image of theanalytic region A₁ of the frame f_(i).

2. Two pixels of each data pair belong to the image of the same analyticregion, and belong to the images of different frames. In this case,pairs of data on the pixels in the same analytic region in the images ofdifferent frames are used to perform a correlation calculation. Thiscorrelation calculation is a cross-correlation calculation.

$\begin{matrix}{{G_{3{sdc}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{f_{i}}\left( {x,y,z} \right)}*{{I_{f_{j}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{ij}}}}{\left( {\sum{{I_{f_{i}}\left( {x,y,z} \right)}/M_{i}}} \right)\left( {\sum{{I_{f_{j}}\left( {x,y,z} \right)}/M_{ij}}} \right)}} & (6)\end{matrix}$where G_(3sdc) is a cross-correlation value in the same analytic regionA₁ of a frame f_(i) and a frame f_(i) that are different from eachother, I_(fi) is data, for example, fluorescence intensity data on thepixels of the image of the analytic region A₁ of the frame f_(i), I_(fj)is data, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₁ of the frame f_(j), x, y, z are spatialcoordinates of a measurement point, ξ, ψ, η are variations of thespatial coordinates from the measurement point, M_(ij) is the number ofproduct-sum calculations of the data on the pixels of the image of thesame analytic region A₁ of the frame f_(i) and frame f_(j), M_(i) is thetotal number of data on the pixels of the image of the analytic regionA₁ of the frame f_(i), and M_(j) is the total number of data on thepixels of the image of the analytic region A₁ of the frame f_(j).

3. Two pixels of each data pair belong to the images of differentanalytic regions, and belong to the image of the same frame. In thiscase, pairs of data on the pixels in different analytic regions in theimage of the same frame are used to perform a correlation calculation.This correlation calculation is a cross-correlation calculation.

$\begin{matrix}{{G_{3{dsc}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y,z} \right)}*{{I_{2f_{i}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{12{ii}}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y,z} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{i}}\left( {x,y,z} \right)}/M_{2i}}} \right)}} & (7)\end{matrix}$where G_(3dsc) is a cross-correlation value between different analyticregions A₁ and A₂ of the same frame f_(i), I_(1fi) is data, for example,fluorescence intensity data on the pixels of the image of the analyticregion A₁ of the frame f_(i), I_(2fi) is data, for example, fluorescenceintensity data on the pixels of the image of the analytic region A₂ ofthe frame f_(i), x, y, z are spatial coordinates of a measurement point,ξ, ψ, η are variations of the spatial coordinates from the measurementpoint, M_(12ii) is the number of product-sum calculations of the data onthe pixels of the images of the different analytic regions A₁ and A₂ ofthe frame f_(i), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2i) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(i).

4. Two pixels of each data pair belong to the images of differentanalytic regions, and belong to the image of the different frame. Inthis case, pairs of data on the pixels in different analytic regions inthe images of different frames are used to perform a correlationcalculation. This correlation calculation is a cross-correlationcalculation.

$\begin{matrix}{{G_{3{ddc}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y,z} \right)}*{{I_{2f_{j}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{12{ij}}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y,z} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{j}}\left( {x,y,z} \right)}/M_{2j}}} \right)}} & (8)\end{matrix}$where G_(3ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fj) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y, z are spatialcoordinates of a measurement point, ξ, ψ, η are variations of thespatial coordinates from the measurement point, M_(12ij) is the numberof product-sum calculations of the data on the pixels of the images ofthe analytic region A₁ of the frame f_(i) and the analytic region A₂ ofthe frame f_(j), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2j) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(j).

The data on each pixel used in the correlation calculation may be thedata on this pixel, or may be the statistics of data on multiple pixelsincluding the above pixel. The multiple pixels may be, for example, apixel of interest and a pixel adjacent thereto. The statistics may beany one of, for example, the average value, maximum value, minimumvalue, relative difference, absolute difference, and relative ratio ofthe data on the pixels. Which statistics to use is determined by whichkind of information to be obtained by the analysis according to theRICS.

The data used in the correlation calculation may be a pixel time, a linetime, a frame time, a pixel position relation, a pixel size, or thestatistics thereof.

Regarding the correlation calculation, each image is reconstructed onthe basis of data on the pixels, and a correlation calculation may beperformed for the reconstructed image. For example, the data on theadjacent pixels may be added together to reduce the number of data onthe pixels to half. Alternatively, the data on one pixel is divided intomultiple data. Normally, the number of data on a pixel does not increaseonce an image is acquired. However, on the assumption that the intensityof the acquired data on the pixel is spread around this data on thepixel by the Gaussian distribution, data on the pixel that are notnormally acquired are supplemented. The number of data on the pixel doesnot increase in essence, but the image appears better.

(Step S6)

A fitting is performed for the result of the correlation calculation inStep 5. Thus, at least one of the number of molecules and a diffusiontime is estimated. The calculation formula to be applied to the fittingvaries by whether the image of the analytic region is a two-dimensionalimage or a three-dimensional image.

The calculation formula to be applied to the two-dimensional image is asfollows.

$\begin{matrix}{\mspace{79mu}{{{G_{s}\left( {\xi,\psi} \right)} = {{S\left( {\xi,\psi} \right)}*{G\left( {\xi,\psi} \right)}}}\mspace{79mu}{{S\left( {\xi,\psi} \right)} = {\exp\left( {- \frac{\frac{1}{2}*\left\lbrack {\left( \frac{2{\xi\delta}_{r}}{W_{0}} \right)^{2} + \left( \frac{2{\psi\delta}_{r}}{W_{0}} \right)^{2}} \right\rbrack}{\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi}} \right)}}{W_{0}^{2}}} \right)}} \right)}}{{G\left( {\xi,\psi} \right)} = {\frac{1}{N}\left( {\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi}} \right)}}{W_{0}^{2}}} \right)^{- 1}*\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi}} \right)}}{W_{Z}^{2}}} \right)^{{- 1}/2}} \right)}}}} & (9)\end{matrix}$where G_(s) is a spatial correlation value of RICS, S is the influenceof a scan in an analysis of the RICS, G is the influence of a time delayin the analysis of the RICS, D is a diffusion constant, δ_(r) is a pixelsize, N is the number of molecules, ξ, ψ are variations of spatialcoordinates, W₀ is the lateral radius of an excitation laser beam, W_(Z)is the longitudinal radius of the excitation laser beam, τ_(p) is apixel time, τ_(l) is a line time, and τ_(f) is a frame time.

The calculation formula to be applied to the three-dimensional image isas follows.

$\begin{matrix}{\mspace{79mu}{{{G_{s}\left( {\xi,\psi,\eta} \right)} = {{S\left( {\xi,\psi,\eta} \right)}*{G\left( {\xi,\psi,\eta} \right)}}}\mspace{79mu}{{S\left( {\xi,\psi,\eta} \right)} = {\exp\left( {- \frac{\frac{1}{2}*\left\lbrack {\left( \frac{2\xi\;\delta_{r}}{W_{0}} \right)^{2} + \left( \frac{2{\psi\delta}_{r}}{W_{0}} \right)^{2} + \left( \frac{2{\eta\delta}_{r}}{W_{0}} \right)^{2}} \right\rbrack}{\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi} + {\tau_{f}\eta}} \right)}}{W_{0}^{2}}} \right)}} \right)}}{{G\left( {\xi,\psi,\eta} \right)} = {\frac{1}{N}\left( {\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi} + {\tau_{f}\eta}} \right)}}{W_{0}^{2}}} \right)^{- 1}*\left( {1 + \frac{4{D\left( {{\tau_{p}\xi} + {\tau_{l}\psi} + {\tau_{f}\eta}} \right)}}{W_{Z}^{2}}} \right)^{{- 1}/2}} \right)}}}} & (10)\end{matrix}$where G_(s) is a spatial correlation value of RICS, S is the influenceof a scan in an analysis of the RICS, G is the influence of a time delayin the analysis of the RICS, D is a diffusion constant, δ_(r) is a pixelsize, N is the number of molecules, ξ, ψ, η are variations of spatialcoordinates, W₀ is the lateral radius of an excitation laser beam, W_(Z)is the longitudinal radius of the excitation laser beam, τ_(p) is apixel time, τ_(l) is a line time, and τ_(f) is a frame time.

The number of molecules and the diffusion constant are found by aresidual comparison (fitting) between the theoretical values in Equation(1) to Equation (8) and the results of the correlation calculations thatuse measured values. In the fitting, first, (a) a predetermineddiffusion constant D and the number of molecules N are used to calculateG_(s) (hereinafter, a theoretical correlation value G_(s)), which isobtained as a theoretical value. (b) The theoretical correlation valueG_(s) is then compared with a correlation value G_(s), which is obtainedas a measured value (hereinafter, a measured correlation value G_(s)),and a residual therebetween is calculated. (c) The diffusion constant Dand the number of molecules N in the theoretical correlation value G_(s)are then changed to calculate a new theoretical correlation value G_(s).(d) The new theoretical correlation value G_(s) is then compared withthe measured correlation value G_(s), and a residual therebetween iscalculated. (e) The residual that has been obtained in (b) is thencompared with the residual that has been obtained in (d) to judgewhether the residual has increased. Thus, in the fitting, (b) to (e) arerepeated while the diffusion constant D and the number of molecules N inthe theoretical correlation value G_(s) are changed, and a theoreticalcorrelation value G_(s) that provides the minimum residual between themeasured correlation value G_(s) and the theoretical correlation valueG_(s) is finally found. The diffusion constant D and the number ofmolecules N in the finally obtained theoretical correlation value G_(s)are diffusion constant D and the number of molecules N in the measuredcorrelation value G_(s). Thus, the fitting according to Equation (9) orEquation (10) is to estimate the optimum number of molecules ordiffusion constant in the two-dimensional or three-dimensionalobservation region while varying the diffusion constant D and the numberof molecules N in the theoretical correlation value G_(s).

There is a relation represented by Equation (11) between the diffusionconstant and the diffusion time. Therefore, the diffusion time can befound from the found diffusion constant.τ=W ₀ ²/4D  (11)

(Step S7)

The analytic result, for example, the image of the number of moleculesor the diffusion constant is saved. If necessary, the image of thenumber of molecules or the diffusion constant may be displayed. Theanalytic result may be displayed after the end of the analyses for allthe time intervals. An example of the analytic result is shown in FIG.12 and FIG. 13. FIG. 12 shows an example of how a calculation result ofa spatial correlation value regarding molecules in the sample S isdisplayed as an image. FIG. 13 shows a fitting result of the calculationresult of the spatial correlation value in FIG. 12. In FIG. 12, themagnitude of the spatial cross-correlation value is indicated byluminance.

(Step S8)

The analysis for one time interval is finished by the operations in StepS5 to Step S7. The operations in Step S5 to Step S7 are repeated foreach of the time intervals set in Step S4. That is, while the timeintervals that have not been applied to the analysis still remain, thetime interval applied to the analysis is changed to return to Step S5.In other words, a correlation calculation is performed for each of thetime intervals, and each of the results of the correlation calculationsis fitted.

The analytic result for a short time interval strongly reflects thechange of a molecular species having a low molecular weight. Theanalytic result for a long time interval strongly reflects the change ofa molecular species having a high molecular weight. That is, thecorrelation result for a certain time interval strongly reflects thechange of a molecular species corresponding to this time interval.Therefore, the correlation analysis is performed for each of the timeintervals, so that the change of each of the molecular species can beknown. That is, a multicomponent analysis can be performed.

(Step S9)

If necessary, the ratio of the molecular species in the analytic regionis calculated. The equation to be applied to the calculation is asfollows.

$\begin{matrix}{P_{Ni} = {\frac{N_{i}}{\sum\limits_{k = 1}^{m}N_{k}} \times 100\%}} & (12)\end{matrix}$where N_(i) is the number of molecules of the molecular species of ani-component, P_(Ni) is the ratio of the number of molecules N_(i) in themolecular species of the i-component, N_(k) is the number of moleculesof the molecular species of a k-component, and m is the number ofcomponents in the multicomponent analysis.

According to the present embodiment, motion, for example, can beevaluated regarding different molecules in the sample S. That is, themulticomponent analysis is possible. For example, the motions of themolecules moving at high velocities and the molecules moving at moderatevelocities can be evaluated.

While the embodiments of the present invention has been described so farwith reference to the drawings, the present invention is not limited tothese embodiments, and various modifications and alterations may be madewithout departing from the spirit thereof.

For example, the analysis of the image that is contracted by detectingthe fluorescence generated from the sample S, that is, the fluorescenceimage has been described in the embodiments. However, the image to beanalyzed is not limited to the fluorescence image. Instead of thefluorescence image, the image to be analyzed may be, for example, animage constructed by detecting phosphorescence, reflected light, visiblelight, chemiluminescence, bioluminescence, or scattered light.

Although the image acquired by the raster scan has been described in theembodiments, the image is not limited to the image acquired by theraster scan. The image has only to be an image comprising pixels inwhich data on the pixels are acquired in a time-series manner. The imagemay be an image acquired by some other scanning method. Moreover, theimage may be an image acquired by a two-dimensional image pickup devicesuch as a CCD or a CMOS. In this case, an image of one frame comprisespixels the data of which have been simultaneously acquired, andacquiring images of multiple frames is assumed in Step S1.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

What is claimed is:
 1. An image analysis method comprising: acquiring animage of at least one frame that comprises pixels; setting at least oneanalytic region for the image of at least one frame; extracting data onthe pixel corresponding to each analytic region; setting time intervalsfor data pairs for use in correlation calculations; performing acorrelation calculation for each of the time intervals by use of theextracted data; and performing a fitting for each of the correlationcalculation results, wherein the acquiring the image of the at least oneframe acquires images of frames, and the setting the at least oneanalytic region sets analytic regions for the image of each frame, theanalytic regions being the same regions in the image of each frame,respectively, wherein the performing the correlation calculationincludes performing the correlation calculation by use of pairs of dataon the pixels in different analytic regions in the images of differentframes.
 2. The image analysis method according to claim 1, wherein theimage of the analytic region is a two-dimensional image, and theperforming the correlation calculation performs the correlationcalculation by use of the following equation:${G_{2{ddc}}\left( {\xi,\psi} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y} \right)}*{{I_{2f_{j}}\left( {{x + \xi},{y + \psi}} \right)}/M_{12{ij}}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{j}}\left( {x,y} \right)}/M_{2j}}} \right)}$where G_(2ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fj) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y are spatialcoordinates of a measurement point, ξ, ψ are variations of the spatialcoordinates from the measurement point, M_(12ij) is the number ofproduct-sum calculations of the data on the pixels of the images of theanalytic region A₁ of the frame f_(i) and the analytic region A₂ of theframe f_(j), M_(1i), is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2j) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(j).
 3. The image analysis method according to claim1, wherein the image of the analytic region is a three-dimensionalimage, the performing the correlation calculation performs thecorrelation calculation by use of the following equation:${G_{3\;{ddc}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{1\; f_{i}}\left( {x,y,z} \right)}*{{I_{2\; f_{j}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{12\; i\; j}}}}{\left( {\sum{{I_{1\; f_{i}}\left( {x,y,z} \right)}/M_{1\; i}}} \right)\left( {\sum{{I_{2\; f_{j}}\left( {x,y,z} \right)}/M_{2\; j}}} \right)}$where G_(3ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fj) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y, z are spatialcoordinates of a measurement point, ξ, ψ, η are variations of thespatial coordinates from the measurement point, M_(12ij) is the numberof product-sum calculations of the data on the pixels of the images ofthe analytic region A₁ of the frame f_(i) and the analytic region A₂ ofthe frame f_(j), M_(1i), is the total number of data on the pixels ofthe image of the analytic region A₁ of the frame f_(i), and M_(2j) isthe total number of data on the pixels of the image of the analyticregion A₂ of the frame f_(j).
 4. The image analysis method according toclaim 3, wherein the performing the fitting performs the fitting by useof the following equation: G_(S)(ξ, ψ, η) = S(ξ, ψ, η) * G(ξ, ψ, η)${S\left( {\xi,\psi,\eta} \right)} = {\exp\left( {- \frac{\frac{1}{2}*\left\lbrack {\left( \frac{2\;\xi\;\delta_{r}}{W_{0}} \right)^{2} + \left( \frac{2\;\psi\;\delta_{r}}{W_{0}} \right)^{2} + \left( \frac{2\;\eta\;\delta_{r}}{W_{0}} \right)^{2}} \right\rbrack}{\left( {1 + \frac{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}{W_{0}^{2}}} \right)}} \right)}$${G\left( {\xi,\psi,\eta} \right)} = {\frac{1}{N}\left( {\left( {1 + \frac{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}{W_{0}^{2}}} \right)^{- 1}*\left( {1 + \frac{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}{W_{Z}^{2}}} \right)^{{- 1}\text{/}2}} \right)}$where G_(s) is a spatial correlation value of RIGS, S is the influenceof a scan in an analysis of the RIGS, G is the influence of a time delayin the analysis of the RIGS, D is a diffusion constant, δ_(r) is a pixelsize, N is the number of molecules, ξ, ψ, η are variations of spatialcoordinates, W₀ is the lateral radius of an excitation laser beam, W_(Z)is the longitudinal radius of the excitation laser beam, τ_(p) is apixel time, τ_(l) is a line time, and τ_(f) is a frame time.
 5. Theimage analysis method according to claim 1, further comprisingestimating the number of molecules of a molecular species of eachcomponent in the analytic region by performing the fitting, andcalculating the ratio of the molecular species by use of the followingequation:$P_{N\; i} = {\frac{N_{i}}{\sum\limits_{k = 1}^{m}\; N_{k}} \times 100\%}$where N_(i) is the number of molecules of the molecular species of ani-component, P_(Ni) is the ratio of the number of molecules N_(i) in themolecular species of the i-component, N_(k) is the number of moleculesof the molecular species of a k-component, and m is the number ofcomponents in the multicomponent analysis.
 6. The image analysis methodaccording to claim 1, further comprising reconstructing data on thepixels in the analytic region, wherein the performing the correlationcalculation performs the correlation calculation by use of thereconstructed data.
 7. The image analysis method according to claim 1,wherein the image of each frame comprises pixels the data of which areacquired in a time-series manner by light scanning.
 8. The imageanalysis method according to claim 1, further comprising displaying acorrelation calculation result.
 9. An image analysis apparatuscomprising: an image acquiring section to acquire an image of at leastone frame that comprises pixels; an analytic region setting section toset at least one analytic region for the image of at least one frame; adata extracting section to extract data on the pixel corresponding toeach analytic region; a time interval setting section to set timeintervals for data pairs for use in correlation calculations; and ananalytic processing section to perform a correlation calculation foreach of the time intervals by use of the extracted data, and a fittingfor each of the correlation calculation results, wherein the imageacquiring section acquires images of frames, and the analytic regionsetting section sets analytic regions for the image of each frame, theanalytic regions being the same regions in the image of each frame,respectively, wherein the analytic processing section performs thecorrelation calculation by use of pairs of data on the pixels indifferent analytic regions in the images of different frames.
 10. Theimage analysis apparatus according to claim 9, wherein the image of theanalytic region is a two-dimensional image, and the analytic processingsection performs the correlation calculation by use of the followingequation:${G_{2\;{ddc}}\left( {\xi,\psi} \right)} = \frac{\sum{{I_{1f_{i}}\left( {x,y} \right)}*{{I_{2f_{j}}\left( {{x + \xi},{y + \psi}} \right)}/M_{12i\; j}}}}{\left( {\sum{{I_{1f_{i}}\left( {x,y} \right)}/M_{1i}}} \right)\left( {\sum{{I_{2f_{j}}\left( {x,y} \right)}/M_{2j}}} \right)}$where G_(2ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fj) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y are spatialcoordinates of a measurement point, ξ, ψ are variations of the spatialcoordinates from the measurement point, M_(12ij) is the number ofproduct-sum calculations of the data on the pixels of the images of theanalytic region A₁ of the frame f_(i) and the analytic region A₂ of theframe f_(j), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2j) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(j).
 11. The image analysis apparatus according toclaim 9, wherein the image of the analytic region is a three-dimensionalimage, the analytic processing section performs the correlationcalculation by use of the following equation:${G_{3\;{ddc}}\left( {\xi,\psi,\eta} \right)} = \frac{\sum{{I_{1\; f_{i}}\left( {x,y,z} \right)}*{{I_{2\; f_{j}}\left( {{x + \xi},{y + \psi},{z + \eta}} \right)}/M_{12\; i\; j}}}}{\left( {\sum{{I_{1\; f_{i}}\left( {x,y,z} \right)}/M_{1\; i}}} \right)\left( {\sum{{I_{2\; f_{j}}\left( {x,y,z} \right)}/M_{2\; j}}} \right)}$where G_(3ddc) is a cross-correlation value between the analytic regionA₁ of the frame f_(i) and the analytic region A₂ of the same f_(j),I_(1fi) is data, for example, fluorescence intensity data on the pixelsof the image of the analytic region A₁ of the frame f_(i), I_(2fj) isdata, for example, fluorescence intensity data on the pixels of theimage of the analytic region A₂ of the frame f_(j), x, y, z are spatialcoordinates of a measurement point, ξ, ψ, η are variations of thespatial coordinates from the measurement point, M_(12ij) is the numberof product-sum calculations of the data on the pixels of the images ofthe analytic region A₁ of the frame f_(i) and the analytic region A₂ ofthe frame f_(j), M_(1i) is the total number of data on the pixels of theimage of the analytic region A₁ of the frame f_(i), and M_(2j) is thetotal number of data on the pixels of the image of the analytic regionA₂ of the frame f_(j).
 12. The image analysis apparatus according toclaim 11, wherein the analytic processing section performs the fittingby use of the following equation:G_(S)(ξ, ψ, η) = S(ξ, ψ, η) * G(ξ, ψ, η)${S\left( {\xi,\psi,\eta} \right)} = {\exp\left( {- \frac{\frac{1}{2}*\left\lbrack {\left( \frac{2\;\xi\;\delta_{r}}{W_{0}} \right)^{2} + \left( \frac{2\;\psi\;\delta_{r}}{W_{0}} \right)^{2} + \left( \frac{2\;\eta\;\delta_{r}}{W_{0}} \right)^{2}} \right\rbrack}{\left( {1 + \frac{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}{W_{0}^{2}}} \right)}} \right)}$${G\left( {\xi,\psi,\eta} \right)} = {\frac{1}{N}\left( {\left( {1 + \frac{\;{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}}{W_{0}^{2}}} \right)^{- 1}*\left( {1 + \frac{\;{4\;{D\left( {{\tau_{p}\xi} + {\tau_{l\;}\psi} + {\tau_{f}\eta}} \right)}}}{W_{Z}^{2}}} \right)^{{- 1}/2}} \right)}$where G_(s) is a spatial correlation value of RIGS, S is the influenceof a scan in an analysis of the RIGS, G is the influence of a time delayin the analysis of the RIGS, D is a diffusion constant, δ_(r) is a pixelsize, N is the number of molecules, ξ, ψ, η are variations of spatialcoordinates, W₀ is the lateral radius of an excitation laser beam, W_(Z)is the longitudinal radius of the excitation laser beam, τ_(p) is apixel time, τ_(l) is a line time, and τ_(f) is a frame time.
 13. Theimage analysis apparatus according to claim 9, the analytic processingsection estimates the number of molecules of a molecular species of eachcomponent in the analytic region by performing the fitting, andcalculates the ratio of the molecular species by use of the followingequation:$P_{N\; i} = {\frac{N_{i}}{\sum\limits_{k = 1}^{m}\; N_{k}} \times 100\%}$where N_(i) is the number of molecules of the molecular species of ani-component, P_(Ni) is the ratio of the number of molecules N_(i) in themolecular species of the i-component, N_(k) is the number of moleculesof the molecular species of a k-component, and m is the number ofcomponents in the multicomponent analysis.
 14. The image analysisapparatus according to claim 9, the analytic processing sectionreconstructs data on the pixels in the analytic region, and performs thecorrelation calculation by use of the reconstructed data.
 15. The imageanalysis apparatus according to claim 9, wherein the image of each framecomprises pixels the data of which are acquired in a time-series mannerby light scanning.
 16. The image analysis apparatus according to claim9, further comprising a displaying section to display a correlationcalculation result.